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Block #842,529

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/6/2014, 5:08:22 PM Β· Difficulty 10.9736 Β· 6,001,276 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
551d217aa2f1735583f9b9e8a328ee304dbac570ed8e6acbbec316f40fccec38
View on Chainz β†—

Height

#842,529

Difficulty

10.973584

Transactions

1

Size

208 B

Version

2

Bits

0af93cc8

Nonce

205,240,252

Timestamp

12/6/2014, 5:08:22 PM

Confirmations

6,001,276

Merkle Root

9ae36412a9a9677c19fdc803fc4f790c0ed03eb3add3c1585301b4ed1dc2151a
Transactions (1)
Coinbase9ae36412a9a967…01b4ed1dc2151a
1 in β†’ 1 out8.2900 XPM116 B
ANSXnLY2…Sd25TjkD
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.796 Γ— 10⁹⁸(99-digit number)
17966055240435200149…83352928362836019200
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin βˆ’ 1
1.796 Γ— 10⁹⁸(99-digit number)
17966055240435200149…83352928362836019199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.593 Γ— 10⁹⁸(99-digit number)
35932110480870400298…66705856725672038399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.186 Γ— 10⁹⁸(99-digit number)
71864220961740800596…33411713451344076799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.437 Γ— 10⁹⁹(100-digit number)
14372844192348160119…66823426902688153599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.874 Γ— 10⁹⁹(100-digit number)
28745688384696320238…33646853805376307199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.749 Γ— 10⁹⁹(100-digit number)
57491376769392640477…67293707610752614399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.149 Γ— 10¹⁰⁰(101-digit number)
11498275353878528095…34587415221505228799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.299 Γ— 10¹⁰⁰(101-digit number)
22996550707757056191…69174830443010457599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.599 Γ— 10¹⁰⁰(101-digit number)
45993101415514112382…38349660886020915199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.198 Γ— 10¹⁰⁰(101-digit number)
91986202831028224764…76699321772041830399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.839 Γ— 10¹⁰¹(102-digit number)
18397240566205644952…53398643544083660799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 842529

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock 551d217aa2f1735583f9b9e8a328ee304dbac570ed8e6acbbec316f40fccec38

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #842,529 on Chainz β†—
Circulating Supply:57,994,814 XPMΒ·at block #6,843,804 Β· updates every 60s
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